of 1 42
Life and Artificial Intelligence
By
Ian Beardsley
Copyright © 2021 by Ian Beardsley
of 2 42
Contents
Abstract……………………………………..3
Important……………………………………4
The Computation……………………………5
The Dynamic Function……………………..5
Life………………………………………….9
Conclusion…………………………………..9
The Geometric Connection………………….10
Bone As A Mathematical Construct…………12
Life Starts in the Stars……………………….20
Caveman Mathematics And
The Primordial Earth………………………..22
The Primordial Formation of
Sugars And A Caveman’s Perspective………30
The Activation Function…………………….35
Appendix 1………………………………….40
Appendix 2………………………………….41
of 3 42
Abstract
We show there is every reason to consider biological life and AI are not only mathematical constructs, but
that they are described in terms of one another.
of 4 42
Important
Above we see the artificial intelligence (AI) elements pulled out of the periodic table of the elements. As
you see we can make a 3 by 3 matrix of them and an AI periodic table. Silicon and germanium are in
group 14 meaning they have 4 valence electrons and want 4 for more to attain noble gas electron
configuration. If we dope Si with B from group 13 it gets three of the four electrons and thus has a
deficiency becoming positive type silicon and thus conducts. If we dope the Si with P from group 15 it
has an extra electron and thus conducts as well. If we join the two types of silicon we have a
semiconductor for making diodes and transistors from which we can make logic circuits for AI.
As you can see doping agents As and Ga are on either side of Ge, and doping agent P is to the right of Si
but doping agent B is not directly to the left, aluminum Al is. This becomes important. I call (As-Ga) the
differential across Ge, and (P-Al) the differential across Si and call Al a dummy in the differential because
boron B is actually used to make positive type silicon.
That the AI elements make a three by three matrix they can be organized with the letter E with subscripts
that tell what element it is and it properties, I have done this:
Thus E24 is in the second row and has 4 valence electrons making it silicon (Si), E14 is in the first row
and has 4 valence electrons making it carbon (C). I believe that the AI elements can be organized in a 3 by
3 matrix makes them pivotal to structure in the Universe because we live in three dimensional space so
the mechanics of the realm we experience are described by such a matrix, for example the cross product.
Hence this paper where I show AI and biological life are mathematical constructs and described in terms
of one another.
We see, if we include the two biological elements in the matrix (E14) and and (E15) which are carbon and
nitrogen respectively, there is every reason to proceed with this paper if the idea is to show not only are
the AI elements and biological elements mathematical constructs, they are described in terms of one
another. We see this because the first row is ( B, C, N) and these happen to be the only elements that are
not core AI elements in the matrix, except boron (B) which is out of place, and aluminum (Al) as we will
see if a dummy representative, makes for a mathematical construct, the harmonic mean. Which means we
have proved our case because the first row if we take the cross product between the second and third rows
are, its respective unit vectors for the components, meaning they describe them!
E
13
E
14
E
15
E
23
E
24
E
25
E
33
E
34
E
35
of 5 42
The Computation
And silicon (Si) is at the center of our AI periodic table of the elements. We see the biological elements C
and N being the unit vectors are multiplied by the AI elements, meaning they describe them! But we have
to ask; Why does the first row have boron in it which is not a core biological element, but is a core AI
element? The answer is that boron is the one AI element that is out of place, that is, aluminum is in its
place. But we see this has a dynamic function.
The Dynamic Function
The primary elements of artificial intelligence (AI) used to make diodes and transistors, silicon (Si) and
germanium (Ge) doped with boron (B) and phosphorus (P) or gallium (Ga) and arsenic (As) have an
asymmetry due to boron. Silicon and germanium are in group 14 like carbon (C) and as such have 4
valence electrons. Thus to have positive type silicon and germanium, they need doping agents from group
13 (three valence electrons) like boron and gallium, and to have negative type silicon and germanium they
need doping agents from group 15 like phosphorus and arsenic. But where gallium and arsenic are in the
same period as germanium, boron is in a different period than silicon (period 2) while phosphorus is not
(period 3). Thus aluminum (Al) is in boron’s place. This results in an interesting equation.
A = (Al, Si, P )
B = (G a, G e, As)
A ×
B =
B
C
N
Al Si P
G a G e As
= (P ⋅ G a − Al ⋅ A s)
B + (P ⋅ G a − Al ⋅ A s)
C + (A s ⋅ G e − Si ⋅ G a)
N
A = 26.98
2
+ 28.09
2
+ 30.97
2
= 50g /m ol
B = 69.72
2
+ 72.64
2
+ 74.92
2
= 126g /m ol
A ⋅
B = A Bcosθ
cosθ =
6241
6300
= 0.99
θ = 8
∘
A ×
B = A Bsi nθ = (50)(126)si n8
∘
= 877.79
877.79 = 29.6g /m ol ≈ Si = 28.09g /m ol
Si(As − G a) + Ge(P − Al )
SiG e
=
2B
G e + Si
of 6 42
The differential across germanium crossed with silicon plus the differential across silicon crossed with
germanium normalized by the product between silicon and germanium is equal to the boron divided by
the average between the germanium and the silicon. The equation has nearly 100% accuracy:
We found (Beardsley, Mathematical Structure, 2020) that the differential across silicon (P-Al) times
germanium (Ge) over boron (B) plus the differential across germanium (As-Ga) times silicon (Si) over
boron (B) was equal to the harmonic mean between Si and Ge. This was interesting because aluminum is
used as what I called a dummy doping agent element, which when inserted predicts the actually doping
agent boron, that seems out of place in the periodic table where the core artificial intelligence elements are
concerned. This is written:
Thus because boron is out of place we get the harmonic mean between core AI elements Si and Ge on the
right. But one the left we have a difference between doping elements times a ratio plus another difference
between doping agent times a ratio. The ratios are the semiconducting elements. But the one associated
with Ge is multiplied by Si and the one associated with Si is multiplied by Ge. We have seen this pattern
before, it is stokes theorem:
Stokes Theorem states:
Where:
Thus we have…
28.09(74.92 − 69.72) + 72.61(30.97 − 26.98)
(28.09)(72.61)
=
2(10.81)
(72.61 + 28.09)
0.213658912 = 0.21469712
0.213658912
0.21469712
= 0.995
Si
B
(As − G a) +
G e
B
(P − Al ) =
2 SiG e
Si + Ge
∫
S
( ∇ × u ) ⋅ d S =
∮
C
u ⋅ d r
∇ × u =
i
j k
∂
∂x
∂
∂ y
∂
∂z
u
1
u
2
u
3
of 7 42
We know the harmonic mean H of a function is
And, that the arithmetic mean A of a function is
We have
But, we want to use Stokes theorem so we want the integral in the numerator. So, we make the
approximation
And, we have
But, this is only 80% accurate. We find it is very accurate if we say
i
j
k
∂
∂x
∂
∂ y
∂
∂z
0
Si
B
(Ga)z
Si
B
(As)y
=
Si
B
(As − G a)
i
i
j
k
∂
∂x
∂
∂ y
∂
∂z
Ge
B
(Al )z 0
Ge
B
(P)x
=
Ge
B
(P − Al )
j
H =
1
1
b − a
∫
b
a
f (x)
−1
d x
A =
1
b − a
∫
b
a
f (x)d x
Si
B
(As − G a) +
Ge
B
(P − Al ) =
Ge − Si
Ge
Si
dx
x
H ≈ A
∫
1
0
∫
1
0
[
Si
B
(As − G a) +
Ge
B
(P − Al )
]
d x d y ≈
1
Ge − Si
∫
Ge
Si
x d x
of 8 42
Which yields
We have by molar mass
Thus,…
We can break up our integral into two integrals u, and v:
f (x) =
4
5
x
∫
1
0
∫
1
0
[
Si
B
(As − G a) +
Ge
B
(P − Al )
]
d x d y ≈
1
Ge − Si
4
5
∫
Ge
Si
x d x
Si
B
(Ga) =
28.09
10.81
(69.72) = 181.1688g/m ol
Ge
B
(Al ) =
72.61
10,81
(26.98) = 181.2227g/m ol
Si
B
(As) =
28.09
10.81
(74.92) = 194.68111g/m ol
Ge
B
=
72.61
10.81
(30.97) = 208.02328g/m ol
u = 181z
j + 195y
k
v = 181z
i + 208y
k
∫
1
0
∫
1
0
Si
B
(As − G a)d ydz ≈
1
3
1
(Ge − Si )
∫
Ge
Si
x d x
∫
1
0
∫
1
0
Ge
B
(P − Al )d x d z ≈
2
3
1
(Ge − Si )
∫
Ge
Si
yd y
of 9 42
Life
In order to have life you need carbon because it has four valence electrons allowing it to form in
long chains with hydrogen, nitrogen and oxygen. Silicon is in the same group as carbon and
therefore has 4 valence electrons as well. However it cannot form long chains with hydrogen
because in the presence of other elements it reacts with them, like with O2 to make SiO2 or sand.
Silicon has been considered in its possibility to make life along with boron polymers (Mann and
Perry 1986; Trevors 1997a; Williams 1986) with the conclusion that both silicon and boron lack
”replicative potential”.
Conclusion
It would seem boron is on the dividing line between silicon based life as electronic based life,
and biological life. This puts it next to carbon in the periodic table and diagonal to silicon,
aluminum it its place. If we use aluminum as a dummy in the silicon differential, we have a
mathematical function that is the harmonic mean between silicon and germanium. This
mathematical dynamic seems to be integral in the mathematical relationship between AI and
biological life.
Note, I used an older version of the molar mass for Germanium, it has since been more
accurately determined to be 72.64 as opposed to 72.61, which only make the equation more
accurate.
I have also shown that Stokes form of the equation works for the elements in terms of density,
and atomic radius which are not the harmonic mean but geometric and arithmetic means
respectively so the equation takes a generalized form of:
The power mean is obtained by letting
It is the geometric mean if
and by molar mass or
and by density or
and by atomic radius
Are respectively and
∇ ⋅ Q = C f
−1
(
1
n
⋅
n
∑
i=1
f (x
i
)
)
f (x) = x
p
f (x) = log(x)
(As − G a)
(P − Al )
(Al − P)
(Al − P)
(Al − P)
(Ga − As)
ΔE
1
ΔE
2
of 10 42
And, the ratios
and by molar mass or
and by density or
and by atomic radius where C is
Are, quotients , and , respectively, then
The Geometric Connection
Silicon and carbon, the core artificial intelligence biological life elements respectively have a
geometric connection in the 12 sided (regular dodecagon) and 8 sided (regular octagon)
respectively. If the side of a regular dodecagon is the same as the side of a regular octagon and a
silicon atom is inscribed in the regular dodecagon and the carbon atom is inscribed in the regular
octagon, they line up. As seen on the next page…
Si
B
Ge
B
B
2Ge(Ga − As)
Si
B
2Ge(Ga − As)
P
Si
B
Ge
B
Φ
Q
1
Q
2
∇ = (ΔE
1
, ΔE
2
)
Q = (Q
1
, Q
2
)
of 11 42
of 12 42
Bone As A Mathematical Construct
What better place to begin than with than bone as it is the basic framework around which skeletal life is
structured, the vertebrates. Here is what I found in bone as a mathematical construct:
In my exploration of the connection between biological life and AI the most dynamic component is that of
bone. It affords us the opportunity to look at:
Multiplying Binomials
Completing The Square
The Quadratic Formula
Ratios
Proportions
The Golden Ratio
The Square Root of Two
The Harmonic Mean
of 13 42
Density of silicon is Si=2.33 grams per cubic centimeter.
Density of germanium is Ge=5.323 grams per cubic centimeter.
Density of hydroxyapatite is HA=3.00 grams per cubic centimeter.
This is
where
Where HA is the mineral component of bone, Si is an AI semiconductor material and Ge is an AI
semiconductor material. This means
The harmonic mean between Si and Ge is HA,…
This is the sextic,…
Which has a solution
Where x=Si, and y=Ge. It works for density and molar mass. It can be solved with the online Wolfram
Alpha computational engine. But,…
3
4
Si +
1
4
G e ≈ H A
H A = Ca
5
(PO
4
)
3
OH
Si
H A
Si +
[
1 −
Si
H A
]
G e = H A
2 SiG e
Si + Ge
≈ H A
x
2
(x + y)
4
− x y(x + y)
4
+ 2x y
2
(x + y)
3
− 4x
2
y
2
(x + y)
2
= 0
Si
G e
=
1
2 + 1
1
H A
2
Si
2
−
G e
H A
2
Si +
[
G e
H A
− 1
]
= 0
Si =
1
2
G e
±
H A
G e
H A
2
−
4G e
H A
+ 4
Si = G e − H A
of 14 42
Si
H A
Si +
[
1 −
Si
H A
]
G e = H A
Si
2
H A
+ G e −
Si
H A
G e ≈ H A
1
H A
Si
2
−
G e
H A
Si + Ge ≈ H A
1
H A
2
Si
2
−
G e
H A
2
Si +
G e
H A
≈ 1
1
H A
2
Si
2
−
G e
H A
2
Si +
G e
H A
− 1 ≈ 0
1
H A
2
Si
2
−
G e
H A
2
Si +
[
G e
H A
− 1
]
= 0
of 15 42
We see that the square of the binomial is a quadratic where the third term is the square of one half the
middle coefficient. This gives us a method to solve quadratics called completing the square:
(x + a)(x + a) = x
2
+ 2a x + a
2
(x + a)
2
= x
2
+ 2a x + a
2
a x
2
+ bx + c = 0
a x
2
+ bx = − c
x
2
+
b
a
x = −
c
a
(
1
2
b
a
)
2
=
1
4
b
2
a
2
x
2
+
b
a
x +
1
4
b
2
a
2
= −
c
a
+
1
4
b
2
a
2
(
x +
1
2
b
a
)
2
=
b
2
− 4ac
4a
2
x +
b
2a
=
±
b
2
− 4ac
2a
x =
−b
±
b
2
− 4ac
2a
of 16 42
1
H A
2
Si
2
−
G e
H A
2
Si +
[
G e
H A
− 1
]
= 0
x =
−b
±
b
2
− 4ac
2a
a =
a
H A
2
b = −
G e
H A
2
c =
[
G e
H A
− 1
]
b
2
− 4ac =
G e
2
H A
4
− 4
1
H A
2
[
G e
H A
− 1
]
=
G e
2
H A
4
−
4G e
H A
3
+
4
H A
2
=
1
H A
2
[
G e
2
H A
2
−
4G e
H A
+ 4
]
b
2
− 4ac =
1
H A
(
G e
H A
− 2
)
2
x =
Ge
HA
2
±
1
HA
[
Ge
HA
− 2
]
2
HA
2
=
1
2
G e
±
1
2
H A
[
G e
H A
− 2
]
=
1
2
G e
±
1
2
G e − H A
Si =
1
2
G e +
1
2
G e − H A
Si = G e − H A
of 17 42
Si ≈ G e − H A
H A ≈
2 SiG e
Si + Ge
Si ≈ G e −
2 SiG e
Si + Ge
(Si + Ge)Ge
Si + Ge
−
(Si + Ge)Si
Si + Ge
−
2 SiG e
Si + Ge
= 0
G e
2
− 2SiG e − Si
2
Si + Ge
= 0
x
2
− 2x y − y
2
= 0
x
2
− 2x y = y
2
x
2
− 2x y + y
2
= 2y
2
(x − y)
2
= 2y
2
x − y =
±
2y
x = y + 2y
x = y(1 + 2)
x
y
= 1 + 2
y
x
=
1
2 + 1
Si
G e
≈
1
2 + 1
of 18 42
A ratio is and a proportion is which means a is to b as b is to c.
The Golden Ratio
and.
or
a
b
a
b
=
b
c
(
Φ
)
a
b
=
b
c
a = b + c
a c = b
2
c =
b
2
a
a = b +
b
2
a
b
2
a
− a + b = 0
b
2
a
2
− 1 +
b
a
= 0
(
b
a
)
2
+
b
a
− 1 = 0
(
b
a
)
2
+
b
a
+
1
4
= 1 +
1
4
(
b
a
+
1
2
)
2
=
5
4
b
a
= −
1
2
±
5
2
b
a
=
5 − 1
2
a
b
=
5 + 1
2
ϕ =
5 − 1
2
Φ =
5 + 1
2
ϕ =
1
Φ
of 19 42
The mineral component of bone hydroxyapatite (HA) is
The organic component of bone is collagen which is
We have
%
Ca
5
(PO
4
)
3
OH = 502.32
g
m ol
C
57
H
91
N
19
O
16
= 1298.67
g
m ol
Ca
5
(PO
4
)
3
OH
C
57
H
91
N
19
O
16
= 0.386795722
ϕ = 0.618033989
1 − ϕ = 0.381966011
Ca
5
(PO
4
)
3
OH
C
57
H
91
N
19
O
16
≈ (1 − ϕ)
0.381966011
0.386795722
100 = 98.75
Si
G e
=
28.09
72.61
= 0.386861314 ≈ (1 − ϕ)
Si
G e
≈
Ca
5
(PO
4
)
3
OH
C
57
H
91
N
19
O
16
of 20 42
Life Starts In The Stars
Silicon being inscribed in the twelve-sided polygon represents carbon, because carbon is six
protons and six neutrons. However carbon being inscribed in the eight-sided polygon is
beryllium 8 because it is made from it. See below…
of 21 42
We have that at the beginning of the Universe hydrogen and helium were created. Then the stars formed
and synthesized these into the heavier elements. I find if we include in the category of life not just the
biological elements, but the AI elements, we can find a mathematical equation for a pattern in the periodic
table of the elements that predicts the synthesis of such elements in stars. For instance, Beryllium 8 plus
helium 4 synthesizes to make the biological core element carbon C. Magnesium plus helium 4
synthesized to make the core AI element silicon Si. If we say that Element 4 is Beryllium Be and write it
, and helium He is element 2 and write it , and use this convention for all of the elements, we have
for the production of these elements by stars, and their molar masses in the periodic table the following
equation:
E
4
E
2
E
2n−2
+ E
2
= E
2i−2
= (4k + 4)g /m ol
n = (3,4, 5,6, …)
i = (4,5, 6,7, …)
k = (2,3, 4,5, …)
of 22 42
Caveman Mathematics And The Primordial Earth
One of the mysteries of how life on earth began is how the amino acids, the building blocks of
life were made. Miller and Urey showed if they mixed together the substances of the primordial
earth methane (CH4) ammonia (NH3) and water (H2O) under electricity (to mimic electrical
storms) they could produce ten of the twenty amino acids present in proteins.!
What better way to understand the primordial earth than by way of the primordial caveman?!
Thus at first glance how does a caveman look at the structure of the primordial gas methane
(CH4)? Well CH4 is carbon (C) which is (has 4 valence electrons for bonding). And, is H4
which means there are 4 hydrogen atoms that connect to it. But hydrogen (H) is meaning
for CH4 to be neutral it needs . So we have the chemical structure of methane is:!
!
A carbon surrounded by by four hydrogens in single bonds. The
caveman asks how four things fit around one? Being smart he says
a square tiled by four regular octagons:!
!
Never mind that a carbon atom C is much larger than a hydrogen
atom H…!
So therefore it would be more accurately represented by a carbon atom at the center
surrounded four hydrogen atoms as squares, the carbon atom the regular octagon, the exact
inversion:!
Which actually closely represents the relative sizes of carbon and
hydrogen if they are circles inscribed in them.!
Let us compute the scenario of our caveman’s desire to see carbon tiled by hydrogen without
leaving gaps:"
C
4−
H
1+
4H
+
of 23 42
!
For the square the hydrogen has a radius given by the
apothem, a, of the square. The diagonal of the square is
so the radius of it is .!
!
!
!
It is obvious from the drawing that the apothem is 1/2, but we are warming-up to calculating
the apothem for a regular octagon. It is…!
!
The apothem of a regular octagon is the diameter d divided
by 2. The side of the octagon is 1. Because it connects with
the square. We have if the side is s, that…!
!
!
!
!
!
Thus…!
r
H
2
2/2
(
1
2
)
2
+ a
2
=
(
2
2
)
2
1
4
+ a
2
=
2
4
a =
1
2
d = s + 2x
x
2
+ x
2
= s
2
2x
2
= 1
2
x
2
=
1
2
x =
2
2
of 24 42
!
!
!
!
Is the apothem of the regular octagon.!
We then ask, how can methane be a central carbon as a square surrounded by four regular
octagons and be a regular octagon surrounded four hydrogens. One is much larger than the
other? Let us say they are oscillating between two states as the caveman would have it:!
1 + 2x = d
1 + 2
2
2
= d
d = 1 + 2
a =
2 + 1
2
of 25 42
So if the apothem (a) of the regular octagon becomes the apothem of the square then the
regular octagon expands greatly, as seen here…!
!
Thus if…!
!
!
!
!
"
a =
2 + 1
2
⟶ a
2
+ a
2
=
(
s
2
)
2
( 2 + 1)
2
=
s
2
4
4(2 2 + 3) = s
2
s = 8 2 + 12
s = 4.83
of 26 42
The the apothem of the regular octagon becomes…!
The apothem has gone from 1.207 to 4.1221 and this is an increase in size of…"
of 27 42
!
!
!
!
!
!
!
!
!
!
But, the increase in size does not have to be by the apothem of the regular octagon becomes
the apothem of the square, but rather this by a factor of the inverse of the golden ratio. Our
caveman asks if I divide a line such that…!
d = 1 + 2
2d = 2(1 + 2)
d = 2 + 2 2
2d = 5.414
d = 8.2442
2a = 2
( 2 + 1)
2
2 ⋅ 2a = 2( 2 + 1)
4a = 2 2 + 2
4a + d = 4.828 + 8.2442 = 13.0726
of 28 42
!
where !
Then,…!
!
!
!
!
!
!
The golden ratio conjugate.!
So we have,…!
!
Times larger. We have considered the primordial earth gas CH4 (methane) now let us go to
NH3 (ammonia). The caveman suggests the oscillations in the state from CH4 as regular
octagons surrounding a square to regular octagons surrounded by squares is really the change
from air, which is N2 and O2 to the primordial gas NH3. Dry air at standard temperature and
pressure at sea level 22 degrees C and 1.013 bar is a density of 1.225 kilograms per cubic
meter. Ammonia gas (NH3) at boiling point and 1.013 bar is 0.86 kilograms per cubic meter.
Thus,…!
!
Is approximately our 1.5 above. This is more exactly an accuracy of .
Which is 95.456%"
a
b
=
b
c
a = b + c
ac = b
2
c = a − b
a(a − b) = b
2
a
2
b
2
−
a
b
− 1 = 0
a
b
= Φ =
5 + 1
2
ϕ =
1
Φ
=
b
a
=
5 − 1
2
13.0726
5.414
ϕ = 2.41(0.618) = 1.5
1.225
0.86
= 1.4
1.4244
1.4922
= 0.95456
of 29 42
Thus, what has our caveman done?!
!
He has shown that dry air to NH3 (ammonia) is the geometric inverse by density of methane
(CH4).!
He has found the geometric composition of the primordial earth.!
We have considered the primordial earth CH4 and NH4, and that leaves H2O (water). This is
simple. With the advent of photosynthesizers the earth filled up with oxygen (they converted
carbon dioxide (CO2) to oxygen gas O2). The present earth atmosphere is basically about 25%
O2 and 75% N2. O=16.00 g/mol and N=14.01 g/mol. Thus air as a mixture is:!
0.25O2 + 0.75N2=air=29.0 g/mol!
H2O=2.02+16.00=18.02 g/mol!
Thus,…!
!
The Golden Ratio."
air
H
2
O
=
29.0
18.02
= 1.61 ≈ Φ
of 30 42
The Primordial Formation of Sugars And A Caveman’s Perspective
As we can account for some of the amino acids, the building blocks of life, in that Miller and
Urey showed ten of the twenty amino acids in proteins can be made by mixing together the
primordial earth substances CH4 (methane) NH3 (Ammonia) and H2O water with a few other
gases that were present, and then applying electricity to simulate electrical storms, we need
not just amino acids to have life but sugars for the DNA and RNA that encode life.!
Sugars are carbohydrates with the formula:!
!
Where n is 2 to 7. n=1 is not a sugar and is called formaldehyde which is:!
!
Which has the same structure as a sugar, which is a monomer from which the sugars form; that
is, sugars are polymers of formaldehyde. For DNA (deoxyribose nucleic acid) and RNA (ribose
nucleic acid) that encode life we need deoxyribose:!
!
And, ribose:!
!
The sugar produced by plants through photosynthesis that serves for its food is glucose
which is n=6 in . To make these sugars formaldehyde first combines to
make the sugar glyceraldehyde (n=3):!
!
Then combines with this. But to explain the origins of life in terms of arising from a primordial
substance, we need to explain how we make formaldehyde.!
Formaldehyde is an intermediate in the combustion or oxidation of methane (one of the
primordial gases that make some of the amino acids). It does not accumulate in the
environment because it is broken down by sunlight or by bacteria in soil and water. It is
produced by the action of sunlight and oxygen on atmospheric methane. In the lab it is stored
as an aqueous solution (formalin) because it polymerizes spontaneously into
paraformaldehyde. It exist in the interstellar medium (the empty space between stars) and is
proposed to be formed there by the hydrogenation of carbon monoxide ice:!
!
!
C
n
(H
2
O)
n
CH
2
O
C
5
H
10
O
4
C
5
H
10
O
5
C
6
H
12
O
6
C
n
(H
2
O)
n
C
3
H
6
O
3
H + CO ⟶ HCO
HCO + H ⟶ CH
2
O
of 31 42
The molecular geometry of formaldehyde is trigonal planar :!
And, has a bond angle of 120 degrees. More precisely of HCO=122 degrees, HCH=116
degrees.!
The molecular geometry of methane and ammonia from which have the amino acids are
tetrahedral and pyramidal, respectively:!
The methane has bond angles of HCH=109.5 degrees and the ammonia has bond angles of
HNH=107.8 degrees with an unshared electron pair attached to the nitrogen.!
If we are to look at formaldehyde thought the eyes of a caveman, so we may look at the
primordial with a mind of primordial times we might imagine he would fit three around one by
either considering triangles around a triangle or squares around a triangle…!
of 32 42
!
The arrangement actually folds to make a tetrahedron:!
!
Which is the structure of ammonia used to make amino acids…!
of 33 42
!
Ammonia in chemistry is called
pyramidal because a tetrahedron is
a kind of pyramid. However,
methane, one of the other
primordial gases that make amino
acids is called tetrahedral because
although its form is:!
!
It can be thought of as a tetrahedron with carbon at its
center. By connecting the base hydrogens with the top
hydrogen. Thus we see that the primordial substance
formaldehyde predicts through its geometric dynamics
the methane and ammonia that are the primordial
substances used to make the building blocks of life.
But we need the formaldehyde to make the sugars for
the DNA and RNA that encode for life. However, it
predicts as well the other primordial substance water
(H2O), because it is bent as it is called in chemistry
which is a triangle, the unfolded geometry of the
tetrahedron as seen through the eyes of a caveman:!
of 34 42
!
H2O has the molecular geometry seen here.
The two lone pairs of electrons on the oxygen
push the hydrogens together creating a
compressed angle of HOH=104.5 degrees
that makes it less than the 120 degree bond
angle one would think it would have from
360/3=120.!
Thus, formaldehyde the primordial substance which is used to make the sugars that make DNA
and RNA that encode life, predicts the primordial substances used to make the amino acids
from which DNA and RNA synthesize the proteins of life."
of 35 42
The Activation Function
In order to determine whether life can arise spontaneously or not, a brief review of what we
know suggests what I call an activation function.!
Miller Urey Chemistry!
Under Nobel prize winner in chemistry (1934) Harold Urey, Stanley Miller a graduate student set
out to see if he mimicked the theoretical primordial Earth, he could produce the 20 amino acids
that are the building block of life. He created the ocean by filling a closed glass container with
water, and coming out of this was a tube that went to a second chamber that mimicked the
primordial earth atmosphere which was methane, ammonia, and hydrogen. As the heated
water vaporized it flowed out of the first chamber and into the second chamber. He passed
electricity through the second chamber to mimic electrical storms or lightning. Between the
first chamber and second he placed a condenser, so when the water vapor rose into it, some of
it would condense into liquid to mimic rain. With this experiment he produced 10 of the 20
biological amino acids. We have yet to find a way to produce all 20 under theoretical primordial
earth conditions.!
Produced!
Glycine, Alanine, Aspartate, Valine, Leucine, Glutamate, Isoleucine, Serine, Proline, Threonine!
Not Produced!
Phenyalanine, Tyrosine, Tryptophan, Histidine, Lysine, Arginine, Cysteine, Methionine,
Asparagine, Glutamine!
H2O!
Water is an extraordinary substance and in order to have life you need it. The earth is not only
the right distance from the sun for water to exist in three phases (ice, vapor, and liquid) but is
also happens to be very plentiful here, it covers three quarters of the planet’s surface and what
is more there are great amounts of it under its surface. Let’s look at some of the properties of
water that it has that allows for life:!
1. Water is solvent meaning it dissolves a great number of substances.!
2. Water is cohesive and adhesive, cohesive because it flows freely, yet adhesive in that can
also adhere to surfaces. Unicellular organisms rely on external water to transport nutrients
and waste while multicellular organisms have internal vessels that use it to do the same.
Because of adhesion and cohesion water can climb up from the roots of a tree to its top by
tension created by water evaporating from its leaves.!
3. Water has a high surface tension meaning plant debris can rest on its surface providing
food and shelter for aquatic life.!
4. Water in its solid phase (ice) is less dense than it is in its liquid phase because when it
freezes it expands meaning it floats on the surface water. If it was not for this life could not
exist on earth because if the ice sank the ponds, lakes, and perhaps even the oceans
would freeze over solid.!
5. Water has a high heat capacity. The specific heat of water is one calorie per gram degree
centigrade which means it takes one calorie to raise the temperature of a gram of it by one
degree centigrade. This keeps the earth relatively cool, and thus life thrives. A lot of the
sunlight’s energy goes into vaporizing it into clouds that would otherwise go into heating
the planet."
of 36 42
Dehydration Synthesis and Hydrolysis!
Let us look at how water synthesizes substances and breaks them down. Take making fat from
glycerol and a fatty acid:!
!
If you heat it you remove an H from the glycerol and an OH (hydroxide) from the fatty acid
which is to remove a water molecule H2O leaving an O in the glycerol and a C in the fatty acid
that joins the glycerol with the fatty acid to make the fat. For hydrolysis you add an OH to the
fatty acid and and H to the glycerol by adding water (H2O) to the fat thus breaking down it
down into a fatty acid and glycerol.!
DNA and RNA!
Life is encoded by DNA (deoxyribose nucleic acid) and RNA (ribonucleic acid) which make
nucleic acids. Each nucleic acid is a monomer in a polymer called a nucleotide. The monomer
consists of a phosphate, a 5 carbon sugar, and a nitrogen containing base. The phosphate is
the phosphate ion . Deoxyribose is the sugar and is in DNA and ribose is the
sugar . The bases are guanine, cytosine, adenine, thymine in DNA and RNA uses
uracil in place of thymine. The phosphate combined with the sugar is the backbone of DNA
and RNA, and the bases are attached to the backbone. There are two back bones running
parallel to one another and the bases of one attach to the bases of the other in a pairing that is
always guanine (G) pairs with cytosine (C) and adenine (A) pairs with thymine (T). It is the
sequencing of these pairings the encodes for life, and the parallel backbones are twisted so
you have a twisted ladder where the base pairings are its rungs. !
Guanine: !
Cytosine: !
Adenine: !
Thymine: , Uracil: !
PO
4
−
C
5
H
10
O
4
C
5
H
10
O
5
C
5
H
5
N
5
O
C
4
H
5
N
3
O
C
5
H
5
N
5
C
6
H
6
N
2
O
2
C
4
H
4
N
2
O
2
of 37 42
"
of 38 42
The Problem!
In order to have life we need to have the nucleic acids, which means we need to have the
bases guanine, cytosine, adenine, thymine, and uracil. Can they arise spontaneously from the
calculated conditions of the primordial earth?!
John Oro in 1961 found amino acids and adenine could form from the mixture of hydrogen
cyanide and ammonia in water. Later researchers found several of the bases needed were
present if they allowed hydrogen cyanide to combine with the ammonia when heated in acid.
The problem is hydrogen cyanide present in the laboratory experiment was hundreds of
thousands of times more concentrated than is calculated to have existed on the primordial
earth surface. Further, hydrogen cyanide cannot be concentrated by the evaporation of sea
water in a tidal pool because it is more volatile than water,.!
Later, Leslie Orgel found that freezing a hydrogen cyanide solution would allow it to form in the
voids between ice crystals, which meant adenine could only form in the frozen polar regions. In
1975 Miller froze the stuff for 27 years, then analyzed it finding small amounts of several of the
bases including the adenine.!
We now know that four molecules of hydrogen cyanide can combine to form
diaminomaleonitrile, then, under sunlight, if it reacts with another molecule of hydrogen
cyanide it produces adenine in 7% yield. But if four molecules react with salt ammonium
formate there is 90% yield of adenine. However, this requires dehydration, by removing two
molecules of water, meaning we need to boil away the water of the solution to dryness.!
The Solution!
Substances and rapid temperature changes (cold for some reactions, warm for others like
dehydration synthesis) that are not present today, nor that we calculate were present in the
primordial earth (like sufficient quantities of hydrogen cyanide) that are needed to account for
a prebiotic pathway to the nucleobases and their combination with phosphates and sugars,
and all of the biological amino acids would suggest there was the presence of what I will call an
activation function. Since these necessary substances are not present today, and cannot be
calculated to have existed a long time ago, I suggest that the activation function was a limiting
factor, that as it activated life from what was present, it depleted determining how much life
was present in the beginning by its total depletion. Once life exists the production of the
nucleic acids is possible because it can now be powered by life’s consumption of
carbohydrates, which only can exist on the earth after the existence of life."
of 39 42
The Activation Function!
I would like to suggest that the prebiotic chemistry might have been passed through an
activation function that disappeared after life was on its way to evolving. !
The problem, then, of answering the question of how life began is one of finding the activation
function and its mechanism by which it takes prebiotic chemistry and activates it (makes it
alive) so it can now self-replicate, and evolve. We assume that as this mechanism activates the
molecules, its mechanism depletes as it activates from what is available. In this sense the
mechanism is a limiting reactant, so it determines how much material is activated before it
depletes completely.!
Logically, the way to determine what this mechanism is, and how it serves as an activation
function is to look for the by-products of the reaction that are left over, and from that, deduce
its nature.!
To do this, we have to look for that thing in our knowledge of the Earth’s history that does not
make sense. This would be in the faint young star paradox. We know that five billion years ago,
when the Earth and Sun first formed, that the sun was 0.7 times its present output and so, the
Earth should have been frozen over, yet, we know it was not. That it had water in its liquid
phase. Thus something was there that is not present today. That something must have been
the mechanism for the activation function that “turned on” prebiotic chemistry.!
If is the activation function, where x is the prebiotic material, and we say is residue of
the reaction, and is the activated substance (life) then,!
!
We know . If we can find in nature, we can deduce .!
I have presented it like this because 1) Life has not been created in the laboratory from scratch
2) New life does not seem to be originating on earth in present times. Therefore, the activation
function is probably not present on Earth today and more than likely disappeared, or depleted
after activating prebiotic chemistry. Life exists, yet we do not know how prebiotic substances
organize into self-replicating systems that evolve. Therefore, we must look for something
concerning the Earth that does not make sense. I suggest that would be the young star
paradox. If the Earth had water in its liquid phase when it should have been frozen over, then
something could have existed then that was a limiting reactant, or something like it, that
activated prebiotic substances, in that it was responsible for warming the earth (perhaps a heat
retaining substance).!
I use the term limiting reactant loosely as well as prebiotic chemistry because one, the reactant
was not necessarily a substance alone, but a manifestation of energy not just necessarily
sunlight incident upon the earth and, the prebiotic chemistry was not necessarily just
substances that existed then from what we have theoretically calculated."
σ (x)
r
l
l + r = σ (x)
l
r
σ (x)
of 40 42
Appendix 1 (Atomic Radii, I used data set 4 for my calculations)
of 41 42
Appendix 2 (The Densities, gram per cubic cm)
of 42 42
The Author